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We discuss the existence of knot solitons (Hopfions) in aSkryme-Faddeev-Niemi-type model on the target space $SU(3)/U(1)^2$, which canbe viewed as an effective theory of both the $SU(3)$ Yang-Mills theory and the$SU(3)$ anti-ferromagnetic Heisenberg model. We derive the knot solitons withtwo different types of ansatz: the first is a trivial embedding configurationof $SU(2)$ into $SU(3)$, and the second is a non-embedding configuration thatcan be generated through the B\"{a}cklund transformation. The resultingEuler-Lagrange equations for both ansatz reduce exactly to those of the $CP^1$Skyrme-Faddeev-Niemi model. We also examine some quantum aspects of thesolutions using the collective coordinate zero-mode quantization method.

$SU(3)$ Knot Solitons: Hopfions in the $F_2$ Skyrme-Faddeev-Niemi model